Non-Cartesian data sets in n-dimensional space occur for various reasons. Those analyzing data often obtain non-Cartesian data in order to simplify their analysis of the data. In addition, for a variety of reasons, engineers design certain acquisition devices to acquire data in non-Cartesian representation. For example, ultrasound detection equipment acquires raw data in polar coordinates. The raw data is then interpolated onto a regular two-dimensional grid.
Another example of non-Cartesian data is a data set acquired along a specified curve in n-dimensional space. In the context of medical imaging, a specified curve can represent a patient's spine. An acquisition device can acquire data, e.g., regularly spaced data, along the specified curve. However, the curve itself is not a Cartesian axis.
When a data analyst wants to analyze or process data sets described using different coordinate systems, the analyst will often laboriously translate each data set into a single coordinate system representation. Thus, there exists a need for appropriate storage formats for data sets described using different coordinate systems. In addition, there exists a need for storage formats that facilitate transformation of stored data sets between Cartesian and non-Cartesian coordinates. There also exists a need for methods and systems that facilitate the fusion or combination of non-Cartesian and Cartesian data sets, particularly when these data sets occupy the same or nearby areas or volumes in n-dimensional space.